A method is developed and validated for approximating continuous smooth distributions of finite strains in the ventricles from the deformations of magnetic resonance imaging (MRI) tissue tagging "tag lines" or "tag surfaces." Tag lines and intersections of orthogonal tag lines are determined using a semiautomated algorithm. Three-dimensional (3-D) reconstruction of the displacement field on tag surfaces is performed using two orthogonal sets of MRI images and employing spline surface interpolation. The 3-D regional ventricular wall strains are computed from an initial reference image to a deformed image in diastole or systole by defining a mapping or transformation of space between the two states. The resultant mapping is termed the measurement analysis solution and is defined by determining a set of coefficients for the approximating functions that best fit the measured tag surface displacements. Validation of the method is performed by simulating tag line or surface deformations with a finite element (FE) elasticity solution of the heart and incorporating the measured root-mean-square (rms) errors of tag line detection into the simulations. The FE-computed strains are compared with strains calculated by the proposed procedure. The average difference between two-dimensional (2-D) FE-computed strains and strains calculated by the measurement analysis was 0.022 +/- 0.009 or 14.2 +/- 3.6% of the average FE elasticity strain solution. The 3-D displacement reconstruction errors averaged 0.087 +/- 0.002 mm or 2.4 +/- 0.1% of the average FE solution, and 3-D strain fitting errors averaged 0.024 +/- 0.011 or 15.9 +/- 2.8% of the average 3-D FE elasticity solution. When the rms errors in tag line detection were included in the 2-D simulations, the agreement between FE solution and fitted solution was 24.7% for the 2-D simulations and 19.2% for the 3-D simulations. We conclude that the 3-D displacements of MRI tag lines may be reconstructed accurately; however, the strain solution magnifies the small errors in locating tag lines and reconstructing 3-D displacements.

There is evidence that appropriate footwear is an important factor in the prevention of foot pain in otherwise healthy people or foot ulcers in people with diabetes and peripheral neuropathy. A standard care for reducing forefoot plantar pressure is the utilization of orthotic devices such as total contact inserts (TCI) with therapeutic footwear. Most neuropathic ulcers occur under the metatarsal heads, and foot deformity combined with high localized plantar pressure, appear to be the most significant factors contributing to these ulcers. In this study, patient-specific finite element models of the second ray of the foot were developed to study the influence of TCI design on peak plantar pressure (PPP) under the metatarsal heads. A typical full contact insert was modified based on the results of finite element analyses, by inserting 4 mm diameter cylindrical plugs of softer material in the regions of high pressure. Validation of the numerical model was addressed by comparing the numerical results obtained by the finite element method with measured pressure distribution in the region of the metatarsal heads for a shoe and TCI condition. Two subjects, one with a history of forefoot pain and one with diabetes and peripheral neuropathy, were tested in the laboratory while wearing therapeutic shoes and customized inserts. The study showed that customized inserts with softer plugs distributed throughout the regions of high plantar pressure reduced the PPP over that of the TCI alone. This supports the outcome as predicted by the numerical model, without causing edge effects as reported by other investigators using different plug designs, and provides a greater degree of flexibility for customizing orthotic devices than current practice allows.

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The primary objective of conservative care for the diabetic foot is to protect the foot from excessive pressures. Pressure reduction and redistribution may be achieved by designing and fabricating orthotic devices based on foot structure, tissue mechanics, and

The definition, essential properties and formulation of hierarchic models for laminated plates and shells are presented. The hierarchic models satisfy three essential requirements: approximability; asymptotic consistency, and optimality of convergence rate. Aspects of implementation are discussed and the performance characteristics are illustrated by examples.

SUMMARYThe principles governing the formulation of hierarchic models for laminated composites are discussed. The essential features of the hierarchic models described herein are: (a) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness, and (b) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity. Examples are presented.

SUMMARYThe solution to the Laplace operator in three-dimensional domains in the vicinity of straight edges is presented as an asymptotic expansion involving eigenpairs with their coe cients called edge ux intensity functions (EFIFs). The eigenpairs are identical to their two-dimensional counterparts over a plane perpendicular to the edge. Extraction of EFIFs however, cannot be obtained in a straightforward manner over this two-dimensional plane. A method based on L 2 projection and Richardson extrapolation is presented for point-wise extraction of EFIFs from p-ÿnite element solutions and illustrated by examples. A similar but more e cient method, based on 'energy projection', for extracting EFIFs is proposed.

This parameter estimation algorithm provides the necessary framework for estimating the nonlinear, anisotropic and non-homogeneous material properties of passive myocardium in health and disease in the in vivo beating heart.